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Self-driving cars are coming, and they’re going to be more connected than anything on the road today. There may come a day when most or all vehicles in a city are self-driving, and they’ll most likely communicate with each other to make traffic move more efficiently. What happens if you hack a few of those cars, though? Researchers from the Georgia Institute of Technology developed a model to predict what would happen as self-driving cars were attacked. They found you’d only have to take out a fraction of vehicles in a city to bring traffic to a complete halt.

The study used Manhattan as the basis of the model, a city that has notoriously snarled traffic without self-driving vehicles. An interconnected autonomous system is naturally more efficient than human drivers, and things are even fine if a few self-driving cars get sidelined by a hack. However, the problem gets exponentially more severe as cars stop obeying the rules.

According to study co-author Skanda Vivek, a single hacked vehicle slows down the traffic in its immediate vicinity. As more vehicles go offline, these slowed areas merge and block the flow of traffic for cars that are still functional. Eventually, you get gridlock, and not even emergency vehicles (which will presumably be driven by humans) can get through.

The team developed this model using a statistical approach called percolation theory, a mathematical tool that describes the behavior of connected clusters. Percolation theory is often used to analyze phase transitions in material science, and traffic can be modeled as a phase transition as well. When it’s moving freely, traffic is like an interconnected liquid with no resistance. Add a few clusters of slowed vehicles, and these individual events can eventually add up to a catastrophic phase transition to “solid” gridlock.

In the study, Manhattan’s traffic undergoes that phase change surprisingly easily. If someone managed to hack just 10 percent of rush hour vehicles, half of Manhattan’s 8,000 streets become inaccessible. That essentially chops the island in half. By the time you reach 20 percent, the island is at a standstill.

Is this a realistic scenario? Imagine one major automaker like Toyota or Ford had an unpatched flaw that led to its autonomous cars being disrupted. That could easily be more than 10 percent of total vehicles on the road. An attacker could also target the interconnected networks that monitor and route self-driving car traffic. The team suggests that cities of the future should use multiple connected vehicle networks, limiting the number of vehicles that can be targeted in a single hack. We’ve got time to figure all of this out — even the best self-driving technologies are years away from universal adoption.